Reason for definition of precomputed reciprocals

Albin Ahlbäck ahlback at lix.polytechnique.fr
Thu Jun 25 09:07:55 CEST 2026


Hi,

I'm currently writing routines for computing integer reciprocals, and 
I'm wondering why the definition is `floor((B^2 - 1) / d) - B' instead 
of `floor(B^2 / d) - B - 1'.  The current definition yields a slightly 
faster final iteration written this way, but seemingly at the cost of 
introducing another branch in the division with precomputed reciprocals.

@Torbjörn and Niels, what is the reason behind this definition?

Best,
Albin


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